# Question: Process Dynamics Control Law help.

1. Aug 9, 2010

### specwarop

1. The problem statement, all variables and given/known data
A crude oil preheater furnace has a simplified mathematical model for the process obtained by applying a steady-state energy balance that requires that: Heat input through fuel = heat required to heat feed from T(i) to T, ie:

$$\lambda$$f.Qf = F.Cp.(T-Ti)

Here, Cp is the specific heat capacity of the crude oil feed.

a) Use this information to derive a control law that, given measurements of the disturbance variable Ti, and assuming that the physical properties of the fuel and the crude oil are available, prescribes how to adjust Qf so that T attains the desired value T*.
b) Identify the potential problems a controller based on such a control law is likely.

Letters in brackets are actually subscript.

2. Relevant equations
Refer equation above.

3. The attempt at a solution
I have attempted this question however I honestly have no idea where to go with it.
I have determined which are input and output variables and which are disturbances. But once I work out the y, u, d deviation variables, I get stuck.
In addition, this above question is from the Ogunnaike book on Process Dynamics, which fails to provide answers in the book, or in an external solution manual. So I am therefore unable to check my answers at all.

Any help appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution